Mechanics · Beginner · ⏱ 20 min

Newton's Cradle

Verify conservation of momentum in elastic collisions. Why does pulling two balls always release exactly two on the other side? Build it and find out.

Step 01

Build the Cradle

Add five identical Circle bodies in a row, each with mass m = 1 kg and radius 0.5 m, touching but not overlapping. Connect each to a fixed anchor directly above with a String constraint (length = 3 m). This suspends them like pendulum bobs.

Note: Set the restitution coefficient (bounciness) to 1.0 on all bodies for a perfectly elastic collision. Friction should be 0. This is the idealised cradle.
Step 02

The 1-Ball Experiment

Lift the rightmost ball to 45° and release. Observe: it swings down, collides, and the leftmost ball launches to the same height. The middle three balls appear stationary. Press Pause at the moment of impact and read the velocity graph — the impulse passes through in microseconds.

Note: This is not magic — it is the only solution that simultaneously conserves both momentum and kinetic energy. Any other outcome (e.g., all five moving slowly) would violate one of those laws.
Step 03

The 2-Ball Experiment

Pull back the two rightmost balls together and release. Two balls launch from the other side. Try to predict: what would happen with three? Verify your prediction. The rule: n balls in → n balls out, always.

Note: Why can't 2 balls in send 1 fast ball out? That would conserve momentum (2mv = 1·v') but not kinetic energy (2·½mv² ≠ ½m(2v)²). Both laws must be satisfied simultaneously.
Step 04

Measure Coefficient of Restitution

Now set the restitution coefficient to 0.8 (slightly inelastic). Release 1 ball. The receiving ball rises, but not quite as high. Measure the ratio of rebound height to initial height — this is e² (where e is the coefficient of restitution).

Step 05

Energy Loss Over Time

With e = 0.95 (very slightly inelastic), run the cradle for 60 seconds. Enable the total KE graph. You will see a staircase pattern — each collision loses a little energy, and the swing amplitude gradually decreases. Real steel balls have e ≈ 0.98.

Key formula:
p = mv (conserved) | KE = ½mv² (conserved for elastic)

Discussion

Questions, corrections, and insights welcome.

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